Very closely related to prismaticum; but triangular portion of tubercle acuminate and shorter, having an irregularly mamillate upper surface, and the acumination ending abruptly in a cartilaginous depression containing a tomentose pulvillus: flowers 2.5 to 3 cm. long, white or pinkish, the sepals brownish. Type, Pringle 2580 in Gray Herb. At Carneros Pass, Coahuila. Specimens examined: Coahuila (Pringle 2580 of 1889). The type of this species was not among the collections received from Cambridge, but a specimen of the same distribution from the National Herbarium shows tubercle dimensions different from those recorded in Dr. Watson's description. In that description the triangular terminal surface is said to be "about an inch broad by one-half inch," which is decidedly different from the equilateral surface of the tubercle of prismaticum. In the National Herbarium specimen of furfuraceum, however, of the same distribution, the surface is almost equilateral, measuring 15 mm. long by 18 mm. wide at base. Without the acuminate upper portion the breadth of the triangular portion would be about double its length. The lower rim of the cup-like depression which terminates the tubercle and contains the pulvillus is sometimes slightly prolonged into a tooth, which in prismaticum becomes the sharp tip of the tubercle. The "minutely furfuraceous-punctulate" character of the tubercle is common to all the species of Anhalonium I have seen, and simply represents the external openings of the remarkably long cuticular passageways to the stomata. 4. Anhalonium pulvilligerum Lem. Cact. (1839). Anhalonium elongatum Salm-Dyck (1850). This seems to be a third grooveless Mexican species. I have seen no specimens, but judge from the description that it differs from the two preceding species chiefly in its less crowded and more elongated tubercles (triangular portion 5 cm. long by 2.5 cm. broad at base), which are covered at apex with a tomentose pulvillus. GEOGRAPHICAL DISTRIBUTION. This curious genus is strictly Mexican, and, so far as at present recorded, is characteristic of Coahuila, but a single species (engelmanni) of the four or five known crossing the Rio Grande in the Great Bend. 3. LOPHOPHORA, gen. nov. Depressed-globose, proliferous and cespitose, tuberculate-ribbed, unarmed plants: tubercles at first conical and bearing at summit a flower-bearing areola with a dense tuft or short pencil of compact erect hairs, when mature becoming broad and rounded (with the remnant of the penicellate tuft as a persistent pulvillus in a small central depression) and coalescing into broad convex vertical ribs: spine bearing areolae obsolete: flowers borne at the summit of nascent tubercles: ovary naked (that is free from scales, but often downy): fruit and seed unknown.